In business applications, there have been tremendous interests in analysing customers' repeated purchase behaviour. Recently, the concepts of periodic pattern and cyclic pattern are used to discover recurring patterns from customer sequence database. Toroslu (2003) proposed cyclic pattern mining, which considers a new parameter, named repetition support, into the mining process. In a customer sequence, the occurrence of a subsequence must satisfy single user-specified repetition minimum support. In real-life applications, however, different items may have different frequencies in the database. If all items are set to have the same minimum repetition support, it may cause rare item problem. To solve this problem, we include the concept of multiple minimum supports (MMS) to allow users to specify multiple minimum item repetition support (MIR) according to the natures of items. In this paper, we first redefine cyclic sequential patterns based on MIR and original form of customer minimum support. A new algorithm, rep-PrefixSpan, is developed to discover complete set of cyclic sequential patterns from sequence database. The experimental result shows that the proposed approach achieves more preferable findings than conventional cyclic pattern mining.